Windows only: We recently featured Universal Androot, an app that rooted quite a few Android phones, but had a few limitations (and is already being patched by Google). Windows program SuperOneClick is the easiest, most universal rooting app we've seen yet.
While Universal Androot had the advantage of being an Android app (so you didn't need your PC to root the phone), Google has already released a patch that fixes the exploit in the Nexus One, and we can only assume the next Android update will fix it for other phones. Furthermore, some phones were unsupported, some phones needed certain builds of Android, and others needed you to tweak certain settings in the app for it to work.
SuperOneClick, on the other hand, works on all Android phones except seven, with little or no work required. Just download it, put your phone in USB debugging mode, plug it in, and go (to put your phone in USB debugging mode, just head to Settings > Applications > Development and check USB Debugging). Also, make sure to unmount your SD card before rooting with SuperOneClick.
Six of the seven incompatible phones (specifically the EVO, Droid Incredible, Desire, Aria, Droid Eris and Wildfire) can all still be rooted with previously mentioned Unrevoked, so if you're in that boat, you still have a perfectly capable one-click rooting solution. Unfortunately, users of the T-Mobile G2 are the only ones currently left out of the party.
SuperOneClick is a free download for Windows only, though a Linux version is planned for the next release and Mac support is on the wishlist. Note that you need an account at the XDA-Developers forums to download the app.Thanks Artem!